Maximilian2

Sorry l'll try to be more clear. I took the picture that rapresent the behaviour of the probability below, the thing I can't understand is that if a particle cross the point x=0 (where there is the step potential) why the probability decrease exponentially after that point? Once the particle overcome the obstacle there shouldn't be any reason that cause a less probable localization of the particle with x -> +∞ if not that the particle stop or reverse, and consequently shouldn't we find the probability constant after x=0? I wanted to know the cause or if i was minunderstanding some concept. 

But in this case the exponential decay probability inside the step would be destroyed, because the same ammount of particles that cross the barrier go to infinity. (I forgot to mention explicity that I'm considering the case where E < V0, with E the energy of the wave-particle).

We know that thanks to the tunnel effect, in the case of a finite potential step and considering a stationary state, when a plane wave encounter the step the probabability that the wave-particle coming from -∞ (where potential is V=0) will be ≠ 0, in particular the wave function will be exponential decay. We can also calculate the probability flux (J) through the potential step and the result is J=0. In my book i read that taking into account all these results, the interpretation that we can give is that considering many particles, a certain percentage will cross the step and after a definite amount of time it will turns back before setting out in the direction where it came from, this vision allow us to justify why J=0. Here is my question: once (and if) the wave-particle cross the potential step, shouldn't continue its path without turning back? There is a cause that force it to reverse the direction and that can be explain from an "intuitive" point of view?